Stochastic Calculus for Fractional Brownian Motion and Applications

• Main Authors: Biagini, Francesca (Author), Hu, Yaozhong (Author), Øksendal, Bernt (Author), Zhang, Tusheng (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: London : Springer London, 2008.
• Series: Probability and Its Applications,
• Subjects: Mathematics.; Applied mathematics.; Engineering mathematics.; Probabilities.; Statistics.; Probability Theory and Stochastic Processes.; Statistics for Business/Economics/Mathematical Finance/Insurance.; Applications of Mathematics.

Fractional Brownian motion (fBm) has been widely used to model a number of phenomena in diverse fields from biology to finance. This huge range of potential applications makes fBm an interesting object of study. fBm represents a natural one-parameter extension of classical Brownian motion therefore...

Table of Contents:

• Fractional Brownian motion
• Intrinsic properties of the fractional Brownian motion
• Stochastic calculus
• Wiener and divergence-type integrals for fractional Brownian motion
• Fractional Wick Itô Skorohod (fWIS) integrals for fBm of Hurst index H >1/2
• WickItô Skorohod (WIS) integrals for fractional Brownian motion
• Pathwise integrals for fractional Brownian motion
• A useful summary
• Applications of stochastic calculus
• Fractional Brownian motion in finance
• Stochastic partial differential equations driven by fractional Brownian fields
• Stochastic optimal control and applications
• Local time for fractional Brownian motion.